Original Contribution: On learning the derivatives of an unknown mapping with multilayer feedforward networks

Authors:
A. Ronald Gallant;Halbert White
Affiliations:
North Carolina State University, USA;University of California, San Diego, USA
Venue:
Neural Networks
Year:
1992

Citing 5
Cited 15

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Abstract

Recently, multiple input, single output, single hidden-layer feedforward neural networks have been shown to be capable of approximating a nonlinear map and its partial derivatives. Specifically, neural nets have been shown to be dense in various Sobolev spaces. Building upon this result, we show that a net can be trained so that the map and its derivatives are learned. Specifically, we use a result of Gallant's to show that least squares and similar estimates are strongly consistent in Sobolev norm provided the number of hidden units and the size of the training set increase together. We illustrate these results by an application to the inverse problem of chaotic dynamics: recovery of a nonlinear map from a time series of iterates. These results extend automatically to nets that embed the single hidden layer, feedforward network as a special case.